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Daily demand pattern of average call per hour in a call center of a major bank (2015) ... Transport Research Forum 2011 Proceedings, Adelaide, Australia.
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International Joint Conference - CIO-ICIEOM-IIE-AIM (IJC 2016) San Sebastián, Spain, July 13-15, 2016

Common Service Demand Pattern for Service Capacity Planning. Yuval Cohen1, Shai Rozenes2, Efrat Perel3, Maya Golan4

Abstract This research is based on analysis of empirical data of various service demand patterns such as banks, hospitals, communications and others. The research findings show similar patterns of demand of various different services in different parts of the world. The double hump demand pattern appears to be a typical pattern for daytime services around the globe having typical peak hours during a workday. Analysis shows a striking demand similarity of the same weekdays, and a significant difference between the demand of workdays and weekend days. The paper discusses ways to efficiently plan the service workforce and capacity based on the relevant demand patterns.

Keywords: Demand pattern, Service capacity, Load pattern, Rush hour, Service level.

1Yuval

Cohen (e-mail: [email protected]) Department of Industrial Engineering, Afeka Tel-Aviv College of Engineering. 38 Mivtsa Kadesh, Tel-Aviv 69988, Israel. 2Shai

Rozenes (e-mail: rozenes@ afeka.ac.il) Department of Industrial Engineering, Afeka Tel-Aviv College of Engineering. Tel-Aviv 69988. 3Efrat

Perel (e-mail: [email protected]) Department of Industrial Engineering, Afeka Tel-Aviv College of Engineering. Tel-Aviv 69988. 4Maya

Golan (e-mail : mayag@ afeka.ac.il) Department of Industrial Engineering, Afeka Tel-Aviv College of Engineering. Tel-Aviv 69988.

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1 Introduction While inventory could be used for satisfying demand, services typically cannot be stored (Shtub and Cohen, 2016). Therefore the daily demand pattern for a particular service reflects the actual load on the system (Daskin, 2011). Plenty of daily service demand patterns were gathered and described for specific products or services, but to the best of our knowledge there was no research effort to find commonality across different organizations or services. In this paper we present characteristic demand behavior for various services. This paper focuses on examination of daily patterns of different services and products in an effort to detect similarities and certain characterizing patterns or phenomena. The research questions are described next.

2 The research questions and hypotheses The following are the research questions we tried to answer in this paper: Question 1: Are there similar daily patterns that characterize different services? Hypothesis: Different services share similar daily patterns. Question 2: Are different days of the work week (Monday to Friday) have different patterns? Hypothesis: Workdays share similar demand pattern. Question 3: Do weekends have different demand profile then work days? Hypothesis: Weekends have different demand pattern than weekends. These hypotheses are checked statistically with high significance level.

3 Finding similarity in patterns In this section we show the similarity of daily demand patterns for services around the world. Figure 1 shows a demand pattern we collected during 2010 at a major hospital in Israel. It clearly shows a double hump pattern of calls.

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Hospital Patient Arrivals per Hour During Workdays of First Two Quarters of 2010 (Israel) Sunday

Monday

Tuesday

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Fig 1. Average hourly arrival rates of patients to an Israeli hospital (annual -2010)

While the workdays in the hospital have very similar behavior, the weekend has a different pattern as shown in figure 2. Hospital Daily Average Arrivals: Saturday (2010) 14 14 12 12 9

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Fig 2. Average hourly arrival rates on Saturdays of patients to an Israeli hospital (annual 2010)

The regular double-hump pattern is found in other home consumption areas such as water, and communications. However, the peaks may shift considerably based on drinking/watering habits as shown in figure 3.

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Fig 3. Daily water consumption in Croatia (Margeta, 2010)

This two peak pattern is even more extreme in road and train traffic where the commute to work and back produces rush hours with sharper peaks (e.g. figures 4 and 5).

Fig 4. Average US daily traffic pattern and the effect of different congestion percentages (Margiotta et al, 1999).

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VISTA07

HIST78

Fig 5. Weekday person trips by car and public transport in Melbourne Statistical Division by quarter-hour, 1978=HIS78 and 2007=VISTA07 (McGeoch, 2011).

Figure 6 shows a striking similarity that exists between the daily traffic pattern and the call intensity to 511 (Traveler information service). Workdays Profile

Fig 6. Hourly call distribution during average workday for 2004 (based on 670,369calls to 511 traveler information) – Source US Department of Transportation (US DOT) Federal Highway Administration report - 2006.

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4. Validation Study To validate our findings we processed annual information collected in the call center of an major Israeli bank. This helped us to examine and validate our assumptions related to the daily demand patterns. The results are depicted in figure 7.

Fig 7. Daily demand pattern of average call per hour in a call center of a major bank (2015)

The two peaks are clearly visible in figure 7. Moreover, the differences between workdays are statistically insignificant (Chi-squared test on deviations from the daily average) with the exception of Sunday (under all standard confidence levels). This justifies planning capacity based on an average workday profile. The corresponding profile is depicted in figure 8. Hospital Daily Average Arrivals: Monday - Thursday (2010) 19 19 15

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Fig 8. Average hourly workday arrival rates to an Israeli hospital (2010)

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5. Discussion The patient arrivals in figure 8 are independent of each other, and such independent processes constitute a non-homogeneous Poisson process [8]. Therefore the hourly averages are also the hourly variances. Thus, using the approximation of the Poisson () distribution to the Normal distribution    ,    helps to





ensure the keeping the desired level of service. For example, if the goal is to give treatment to 95% of the arriving patients within an hour from the arrival, the medical workforce should be able to treat a number of patients that is equal to two standard deviations above the average. Thus, for the morning peak hours of figure 12 the capacity should be based on treating 28 patients per hour 19  2 19  28 , while the evening capacity could be planned for treating 24 patients per hour 16  2 16  24 . To answer the hypothesis regarding the difference of the weekend we tested statistically the weekend profile, and found that it is significantly different than the average workday profile (p